In this work, we focus on a generic state estimation problem placed in the context of a future 5G-inspired C-RAN-based cellular network. We consider an underlying large-scale physical system characterized by the state vector \(\mathbf {s}\)  that contains values of \(N\)  system state variables. The state variables are observed through the set of \(M\)  measurements \(\mathbf {x}\)  of physical quantities collected at the measurement devices spread across the system. This paper considers linear system model in which measured quantities are linear functions of the (sub)set of state variables. Further, we assume measurements are wirelessly communicated across C-RAN-based cellular network. In C-RAN, large number of spatially distributed remote radio heads (RRH) constitutes an ultra-dense RAN infrastructure that receives signals from densely populated MTC devices (e.g., the measurement devices under consideration) [1]}. The signal vector \(\mathbf {y}\)  collected at RRHs is forwarded via backhaul links to a central C-RAN location where it is fed into a collection of base-band units (BBU) for signal detection and recovery. In the standard C-RAN signal detection problem, the goal is to recover the signal \(\mathbf {x}\)  transmitted by the set of MTC devices from the signal \(\mathbf {y}\)  received at RRHs and gathered centrally at BBUs [2]}[3]}. However, in this paper, focusing on widely applicable linear system state estimation, we extend this goal and investigate the problem of recovering the system state \(\mathbf {s}\)  directly from the signal \(\mathbf {y}\)  collected across the C-RAN.
